Cellularity of the lowest two-sided ideal of an affine Hecke algebra

Jeremie Guilhot (1)

1 Algebre

In this paper we show that the lowest two-sided ideal of an affine Hecke algebra is affine cellular for all choices of parameters. We explicitely describe the cellular basis and we show that the basis elements have a nice decomposition when expressed in the Kazhdan-Lusztig basis. In type $A$ we provide a combinatorial description of this decomposition in term of number of paths.

Mots clés: Kazhdan-Lusztig Theory; affine Weyl groups; affine cellularity; lowest two-sided cell

Domaines: Théorie des représentations [math.RT]; Combinatoire [math.CO]

Jeremie Guilhot. Cellularity of the lowest two-sided ideal of an affine Hecke algebra. Advances in Mathematics, 2014, 255, pp.525-561. ⟨hal-00790711v2⟩